Related papers: A general proof certification framework for modal …
CoqQ is a framework for reasoning about quantum programs in the Coq proof assistant. Its main components are: a deeply embedded quantum programming language, in which classic quantum algorithms are easily expressed, and an expressive…
Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion…
Formal verification provides mathematical guarantees that a software is correct. Design-level verification tools ensure software specifications are correct, but they do not expose defects in actual implementations. For this purpose,…
A compiler consists of a sequence of phases going from lexical analysis to code generation. Ideally, the formal verification of a compiler should include the formal verification of each component of the tool-chain. An example is the…
The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…
As large language models become integral to high-stakes applications, ensuring their robustness and fairness is critical. Despite their success, large language models remain vulnerable to adversarial attacks, where small perturbations, such…
Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to…
First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing…
In this report we describe a tool framework for certifying properties of PLCs: CERTPLC. CERTPLC can handle PLC descriptions provided in the Sequential Function Chart (SFC) language of the IEC 61131-3 standard. It provides routines to…
In the field of Business Process Management formal models for the control flow of business processes have been designed since more than 15 years. Which methods are best suited to verify the bulk of these models? The first step is to select…
The success of several constraint-based modeling languages such as OPL, ZINC, or COMET, appeals for better software engineering practices, particularly in the testing phase. This paper introduces a testing framework enabling automated test…
A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the…
Large language models (LLMs) have recently demonstrated remarkable progress in formal theorem proving. Yet their ability to serve as practical assistants for mathematicians, filling in missing steps within complex proofs, remains…
Automated theorem proving with large language models in Lean 4 is commonly approached through either step-level tactic prediction with tree search or whole-proof generation. These two paradigms represent opposite granularities for…
Our research is part of a wider project that aims to investigate and reason about the correctness of scheme-based source code transformations of Erlang programs. In order to formally reason about the definition of a programming language and…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
Interactive theorem proving software is typically designed around a trusted proof-checking kernel, the sole system component capable of authenticating theorems. Untrusted automation procedures reside outside of the kernel, and drive it to…
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language,…
We introduce lower-bound certificates for classical planning tasks, which can be used to prove the unsolvability of a task or the optimality of a plan in a way that can be verified by an independent third party. We describe a general…